Lyophilized allografts without pre-treatment with glutaraldehyde are more suitable than cryopreserved allografts for pulmonary artery reconstruction

Various methods are available for preservation of vascular grafts for pulmonary artery (PA) replacement. Lyophilization and cryopreservation reduce antigenicity and prevent thrombosis and calcification in vascular grafts, so both methods can be used to obtain vascular bioprostheses. We evaluated the hemodynamic, gasometric, imaging, and macroscopic and microscopic findings produced by PA reconstruction with lyophilized (LyoPA) grafts and cryopreserved (CryoPA) grafts in dogs. Eighteen healthy crossbred adult dogs of both sexes weighing between 18 and 20 kg were used and divided into three groups of six: group I, PA section and reanastomosis; group II, PA resection and reconstruction with LyoPA allograft; group III, PA resection and reconstruction with CryoPA allograft. Dogs were evaluated 4 weeks after surgery, and the status of the graft and vascular anastomosis were examined macroscopically and microscopically. No clinical, radiologic, or blood-gas abnormalities were observed during the study. The mean pulmonary artery pressure (MPAP) in group III increased significantly at the end of the study compared with baseline (P=0.02) and final [P=0.007, two-way repeat-measures analysis of variance (RM ANOVA)] values. Pulmonary vascular resistance of groups II and III increased immediately after reperfusion and also at the end of the study compared to baseline. The increase shown by group III vs group I was significant only if compared with after surgery and study end (P=0.016 and P=0.005, respectively, two-way RM ANOVA). Microscopically, permeability was reduced by ≤75% in group III. In conclusion, substitution of PAs with LyoPA grafts is technically feasible and clinically promising.

Altered mean platelet volume in patients with polymyositis and its association with disease severity

Polymyositis (PM) is an autoimmune disease characterized by chronic inflammation in skeletal muscle. Mean platelet volume (MPV), a marker in the assessment of systemic inflammation, is easily measured by automatic blood count equipment. However, to our knowledge, there are no data in the literature with respect to MPV levels in PM patients. Therefore, in this study we aimed to investigate MPV levels in patients with PM. This study included 92 newly diagnosed PM patients and 100 healthy individuals. MPV levels were found to be significantly lower compared with healthy controls (10.3±1.23 vs 11.5±0.74 fL, P<0.001). Interestingly, MPV was found to be positively correlated with manual muscle test (MMT) score and negatively correlated with erythrocyte sedimentation rate (ESR) in patients with PM (r=0.239, P=0.022; r=−0.268, P=0.010, respectively). In addition, MPV was significantly lower in active PM patients compared with inactive PM patients (9.9±1.39 vs 10.6±0.92 fL, P=0.010). MPV was independently associated with PM in multivariate regression analyses, when controlling for hemoglobin and ESR (OR=0.312, P=0.031, 95%CI=0.108 to 0.899). The ROC curve analysis for MPV in estimating PM patients resulted in an area under the curve of 0.800, with sensitivity of 75.0% and specificity of 67.4%. Our results suggest that MPV is inversely correlated with disease activity in patients with PM. MPV might be a useful tool for rapid assessment of disease severity in PM patients.

Analysis of Brazilian consumer preference of filled chocolate

Chocolate is the most popular product made from cocoa. It is mainly consumed with fillings, such as fondant, hydrogenated fat or fruits. This work aimed at assessing the sensory acceptability of chocolate filled with strawberry, orange or passion fruit pulps, mixed in fondant, in a hydrogenated fat base and as truffles. Ninety four consumers participated in the test using a 10 cm hedonic scale to rate the overall liking of the samples. Two-way analysis of variance and the Internal Preference Mapping technique were used to analyze the data. Results showed a good overall liking for almost all samples, especially for strawberry and passion fruit truffles, which obtained 8.4 and 8.8 global means, respectively (p < 0.05), in liking ratings, followed by the hydrogenated fat and fondant fillings. The Internal Preference Map presented two dimensions explaining 72.5% of the variation found. Regarding the flavors, strawberry - traditional in chocolate and confectionary in Brazil - and passion fruit obtained better acceptance, unlike the orange fillings, which showed significantly lower ratings (p < 0.05). The orange fondant filling obtained a global mean of 6.5.

Optimizing counterparty credit risk portfolio by reducing exposure at default variance

Rahoitusyhtiöt pitävät omaa pääomaa taseessa harvinaisen suuria markkinamuutoksia varten ja tämän pääoman määrä on ohjattu valvontaviranomaisten toimesta. Euroopassa Basel akordi antaa suuntaviivat näille säädöksille. 2007 vuoden finanssikriisin jälkeen rahoitusyhtiöt sekä valvojat ovat olleet entistä kiinnostuneempia pääoman riittävyydestä. Tutkimuksia riskistä, säädöksistä ja pääomavaateen madaltamisesta on tehty aikaisemmin, mutta tässä tutkimuksessa keskitytään vaateen jatkuvan muutoksen suuruuteen. Tutkimus sisältää hypoteettisen vastapuoliriski portfolion, jossa on mukana valuuttajohdannaisia. Tätä portfoliota simuloidaan eri tavoin, jotta nähtäisiin kuinka suuri vaikutus portfolion koostumuksella voi olla pääomavaateen varianssiin. Jos tämä muuttuja on merkittävä, pitäisikö rahoitusyhtiöiden yrittää pienentää muutosta, jotta yhtiöiden varapääoman määrää voitaisiin alentaa? Tutkimuksessa on myös haastateltu Suomen johtavia vastapuoliriski asiantuntijoita, jotta nähtäisiin rahoitusalan oma näkemys asian merkittävyydestä. Tutkimusmenetelminä toimivat haastattelut sekä numeerinen analyysi hypoteettisella portfoliolla. Kaupat tähän vastapuoliriski portfolioon on luotu 14 vuoden ajalle ja se sisältää ainoastaan valuuttajohdannaisia viidessä eri valuutassa. Riski lasketaan markkina-arvo menetelmällä, joista lasketaan VaR-mallilla tulevaisuuden riski nettoutuksen kera. Portfolion rakennetta muutetaan simuloinneissa, jotta nähtäisiin vaikutus tulevaisuuden riskeille, joita käytetään edustamaan pääomavaateen määrää ja sen vaihtelua yli ajan. Portfolioiden riskejä lasketaan myös rasituskokeiden avulla, jotta tuloksista saataisiin mahdollisimman todenmukaisia. Analyyttinen osuus tutkimuksesta näyttää sen, että tämän kaltainen optimointi on suuresti riippuvainen alkuperäisestä portfoliosta, jonka määrittää yleisesti rahoitusyhtiön myyntistrategia. Yleisesti ottaen pääomavaateen varianssin muutos voi simuloinneissa olla melko suurta, varsinkin jos mukaan huomioidaan rasitus testit, puuttuvat tuotteet sekä muut pääomavaateen laskentaan huomioitavat seikat. Haastatteluissa saatiin selville millainen optimointi voisi olla mahdollista todellisuudessa. Huomattiin myös että tämän kaltainen ajattelumalli on jo huomattu alalla ennestään. Jon Gregory jopa mainitsi, että jotkin rahoitusyhtiöt ovat enemmän kiinnostuneita muutosten pienentämisestä kuin itse pääomavaateen suuruudesta. Näyttääkin siltä, että tämän aihepiiri vaatisi entistä enemmän tutkimusta, sillä sitä ei ennestään vielä ole, ja rahoitusyhtiöt ovat jo alkaneet etsimään uusia keinoja selvitäkseen rahoitusalalla, joka on yhä entisestään kilpailullisempi.

Variance reduction properties of dynamic hedging models - empirical evidence from BRICS countries

This Master’s Thesis analyses the effectiveness of different hedging models on BRICS (Brazil, Russia, India, China, and South Africa) countries. Hedging performance is examined by comparing two different dynamic hedging models to conventional OLS regression based model. The dynamic hedging models being employed are Constant Conditional Correlation (CCC) GARCH(1,1) and Dynamic Conditional Correlation (DCC) GARCH(1,1) with Student’s t-distribution. In order to capture the period of both Great Moderation and the latest financial crisis, the sample period extends from 2003 to 2014. To determine whether dynamic models outperform the conventional one, the reduction of portfolio variance for in-sample data with contemporaneous hedge ratios is first determined and then the holding period of the portfolios is extended to one and two days. In addition, the accuracy of hedge ratio forecasts is examined on the basis of out-of-sample variance reduction. The results are mixed and suggest that dynamic hedging models may not provide enough benefits to justify harder estimation and daily portfolio adjustment. In this sense, the results are consistent with the existing literature.

Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.

The effectiveness of a health versus appearance message on pregnant women's intentions to exercise postpartum : the moderating role of self-monitoring

Despite the confimied health benefits of exercise during the postpartum period, many new mothers are not sufficiently active. The present research aimed to examine the effectiveness of 2 types of messages on intention to exercise after giving birth on 2 groups of pregnant women (low and high self-monitors) using the Theory of Planned Behavior as a theoretical basis. Participants were 2 1 8 pregnant women 1 8 years of age and older (Mean age = 27.9 years, SD = 5.47), and in their second or third trimester. Women completed a demographics questionnaire, a self-monitoring (SM) scale and the Godin Leisure Time Exercise Questionnaire for current and pre-pregnancy exercise levels. They then read one of two brochures, describing either the health or appearance benefits of exercise for postpartum women. Women's attitudes, social norms, perceived behavioral control, and intentions to exercise postpartum were then assessed to determine whether one type of message (health or appearance) was more effective for each group. A MANOVA found no significant effect (p>0.05) for message type, SM, or their interaction. Possible reasons include the fact that the two messages may have been too similar, reading any message about exercise may result in intentions to exercise, or lack of attention given to the brochure. Given the lack of research in this area, more studies are necessary to confirm the present results. Two additional exploratory analyses were conducted. Pearson correlations found higher levels of pre-pregnancy exercise and current exercise to be associated with more positive attitudes, more positive subjective norms, higher perceived behavioral control, and higher intention to exercise postpartum. A hierarchical regression was conducted to determine the predictive utility of attitudes, subjective norms, and perceived behavioral control on intention for each self-monitoring group. Results of the analysis demonstrated the three independent variables significantly predicted intention (p < .001) in both groups, accounting for 58-62% of the variance in intention. For low self-monitors, attitude was the strongest predictor of intention, followed by perceived behavioral control and subjective norm. For high self-monitors, perceived behavioral control was the strongest predictors, followed by attitudes and subjective norm. The present study has practical and real world implications by contributing to our understanding of what types of messages, in a brochure format, are most effective in changing pregnant women's attitudes, subjective norm, perceived behavioral control and intention to exercise postpartum and provides ftirther support for the use of the Theory of Planned Behavior with this population.

Determinants of left ventricular mass as measured by Doppler echocardiography in pre-adolescents

This study examined factors contributing to the differences in left ventricular mass as measured by Doppler echocardiography in children. Fourteen boys (10.3 ± 0.3 years of age) and 1 1 girls (10.5 ± 0.4 years of age) participated in the study. Height and weight were measured, and relative body fat was determined from the measurement of skinfold thickness according to Slaughter et al. (1988). Lean Body Mass was then calculated by subtracting the fat mass from the total body mass. Sexual maturation was self-assessed using the stages of sexual maturation by Tanner (1962). Both pubic hair development and genital (penis or breast for boys and girls respectively) development were used to determine sexual maturation. Carotid Pulse pressure was assessed by applanation tomometry in the left carotid artery. Cardiac mass was measured by Doppler Echocardiography. Images of cardiac structures were taken using B-Mode and were then translated to M- Mode. The dimensions at the end diastole were obtained at the onset of the QRS complex of the electrocardiogram in a plane through a standard position. Measurements included: (a) the diameter of the left ventricle at the end diastole was measured from the septum edge to the endocardium mean border, (b) the posterior wall was measured as the distance from to anterior wall to the epicardium surface, and (c) the interventricular septum was quantified as the distance from the surface of the left ventricle border to the right ventricle septum surface. Systolic time measurements were taken at the peak of the T-wave of the electrocardiogram. Each measurement was taken three to five times before averaging. Average values were used to calculate cardiac mass using the following equation (Deveraux et al. 1986). Weekly physical activity metabolic equivalent was calculated using a standardize activity questionnaire (Godin and Shepard, 1985) and peakV02 was measured on a cycloergometer. There were no significant differences in cardiovascular mesurements between boys and girls. Left ventricular mass was correlated (p<0.05) with size, maturation, peakV02 and physical activity metabolic equivalent. In boys, lean body mass alone explained 36% of the variance in left ventricular mass while weight was the single strongest predictor of left ventricular mass (R =0.80) in girls. Lean body mass, genital developemnt and physical activity metabolic equivalent together explained 46% and 81% in boys and girls, respectively. However, the combination of lean body mass, genital development and peakV02 (ml kgLBM^ min"') explained up to 84% of the variance in left ventricular mass in girls, but added nothing in boys. It is concluded that left ventricular mass was not statistically different between pre-adolescent boys and girls suggesting that hormonal, and therefore, body size changes in adolescence have a main effect on cardiac development and its final outcome. Although body size parameters were the strongest correlates of left ventricular mass in this pre-adolescent group of children, to our knowledge, this is the first study to report that sexual maturation, as well as physical activity and fitness, are also strong associated with left ventricular mass in pre-adolescents, especially young females. Arterial variables, such as systolic blood pressure and carotid pulse pressure, are not strong determinants of left ventricular mass in this pre-adolescent group. In general, these data suggest that although there is no gender differences in the absolute values of left ventricular mass, as children grow, the factors that determine cardiac mass differ between the genders, even in the same pre-adolescent age.

Hydraulic and fluvial geomorphological models for a bedrock channel reach of the Twenty Mile Creek /

Bedrock channels have been considered challenging geomorphic settings for the application of numerical models. Bedrock fluvial systems exhibit boundaries that are typically less mobile than alluvial systems, yet they are still dynamic systems with a high degree of spatial and temporal variability. To understand the variability of fluvial systems, numerical models have been developed to quantify flow magnitudes and patterns as the driving force for geomorphic change. Two types of numerical model were assessed for their efficacy in examining the bedrock channel system consisting of a high gradient portion of the Twenty Mile Creek in the Niagara Region of Ontario, Canada. A one-dimensional (1-D) flow model that utilizes energy equations, HEC RAS, was used to determine velocity distributions through the study reach for the mean annual flood (MAF), the 100-year return flood and the 1,000-year return flood. A two-dimensional (2-D) flow model that makes use of Navier-Stokes equations, RMA2, was created with the same objectives. The 2-D modeling effort was not successful due to the spatial complexity of the system (high slope and high variance). The successful 1 -D model runs were further extended using very high resolution geospatial interpolations inherent to the HEC RAS extension, HEC geoRAS. The modeled velocity data then formed the basis for the creation of a geomorphological analysis that focused upon large particles (boulders) and the forces needed to mobilize them. Several existing boulders were examined by collecting detailed measurements to derive three-dimensional physical models for the application of fluid and solid mechanics to predict movement in the study reach. An imaginary unit cuboid (1 metre by 1 metre by 1 metre) boulder was also envisioned to determine the general propensity for the movement of such a boulder through the bedrock system. The efforts and findings of this study provide a standardized means for the assessment of large particle movement in a bedrock fluvial system. Further efforts may expand upon this standardization by modeling differing boulder configurations (platy boulders, etc.) at a high level of resolution.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Differentiation of morphology and reproductive traits in the house finch (Carpodacus mexicanus): a comparison between native and introduced populations

House Finches (CarpQdacqs mexiCAnuS) were introduced to Long Island, New York from southern'California in 1940. Apparently, an initial sample of less than 100 birds has given rise to a population that now occupies much of the eastern United States. This study was to determine if morphological and reproductive changes have taken place in introduced eastern birds, which have colonized a novel environment. A study area in Goleta, California (CAL) represented the parental population whereas for comparison, House Finches in St. Catharines, Ontario (ONT) represented the introduced population. Interlocality variation in 25 morphometric characters of 100 adult House Finches was examined statistically. Singleclassification analysis of variance revealed significant interlocality differentiation in seven characters of males and nine of females. Females showed differentiation in more limb elements than males. Analysis of character variation using discriminant and principal component analysis distinguished samples on the basis of variation in shape. Compared to CAL, aNT birds (especially females) had smaller extremities relative to certain core parts and weight. Females showed similar patterns of character covariation in each locality on the second principal component, which suggests that differentiation of the ONT population may not be solely environmentally induced. Sexual dimorphism was evident in four charaoters in aNT and five in CAL. Disoriminant analysis distinguished sex on the basis of variation in shape. Males possessed a relatively larger flying apparatus and small.er hind limbs than females. The dearee of sexual dimorphism did not vary sicnifioantly between looalities. 3 Data on reproduotive parameters were oolleoted in 1983 and 1984 in ONT, and 1984 in CAL. In 1984, Bouse Finohes began breedina approximately three months earlier in CAL than in ONT. In ONT, there was no sianifioant differenoe in mean olutoh initiation date between 1983 and 1984. In both looalities most nests oontained either four or five ea",s, and olutoh size differenoes between looalites were not signifioant. Seasonal deolines in olutch size were evident in ONT but not in CAL. Intralooality variation in e.g weight and size was not related to clutch size. E",g weiaht showed no seasonal trend in ONT, but inoreased sianifioantly with breed ina season in OAL. In both looalities e8'''' weiaht increased sipifioantly with order of layina in olutohes of four but not in clutohes of five. Eag's in ONT in 1983 and 1984 were sip.ificantly larser than in CAL in 1984. The modal inoubation period was 13 days and did not vary sip.ifioantly between localites. In both looalities nestling weiaht on the day of hatohing was oorrelated to fresh ega welaht. For muoh of the period between hatohing and 14 days post-hatoh, ONT nestlinas were signifioantly laraer than CAL nestlings in terms of weiaht. bill length, bill depth, and manus length.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Optimization of the valence energy variance of the CuH molecule

We developed the concept of split-'t to deal with the large molecules (in terms of the number of electrons and nuclear charge Z). This naturally leads to partitioning the local energy into components due to each electron shell. The minimization of the variation of the valence shell local energy is used to optimize a simple two parameter CuH wave function. Molecular properties (spectroscopic constants and the dipole moment) are calculated for the optimized and nearly optimized wave functions using the Variational Quantum Monte Carlo method. Our best results are comparable to those from the single and double configuration interaction (SDCI) method.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.